Online Bayesian changepoint detection for network Poisson processes with community structure

TL;DR

This paper introduces an online Bayesian method for detecting changes in the latent community structure of network Poisson processes, enabling rapid and accurate identification of shifts in network behavior in real-time.

Contribution

It presents a scalable variational Bayesian approach with a forgetting factor for online detection of structural changes in network point processes, especially for block-homogeneous Poisson models.

Findings

Successfully detects changes in simulated data

Accurately identifies community shifts in real-world bike-sharing data

Rapidly adapts to changes in network structure

Abstract

Network point processes often exhibit latent structure that govern the behaviour of the sub-processes. It is not always reasonable to assume that this latent structure is static, and detecting when and how this driving structure changes is often of interest. In this paper, we introduce a novel online methodology for detecting changes within the latent structure of a network point process. We focus on block-homogeneous Poisson processes, where latent node memberships determine the rates of the edge processes. We propose a scalable variational procedure which can be applied on large networks in an online fashion via a Bayesian forgetting factor applied to sequential variational approximations to the posterior distribution. The proposed framework is tested on simulated and real-world data, and it rapidly and accurately detects changes to the latent edge process rates, and to the latent node group memberships, both in an online manner. In particular, in an application on the Santander Cycles bike-sharing network in central London, we detect changes within the network related to holiday periods and lockdown restrictions between 2019 and 2020.